Simplify the following expression: $k = \dfrac{10p^2 + 10mp}{12np - 4p} + \dfrac{2np - 6p^2}{12np - 4p}$ You can assume $m,n,p \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{10p^2 + 10mp + 2np - 6p^2}{12np - 4p}$ $k = \dfrac{4p^2 + 10mp + 2np}{12np - 4p}$ The numerator and denominator have a common factor of $2p$, so we can simplify $k = \dfrac{2p + 5m + n}{6n - 2}$